The Study of Superconductivity with Novel Electronic Wave Functions

Abstract

In this thesis we study three examples, where novel superconducting properties all arise from normal state electron wave functions.

In Chapter 2, we study chiral Majorana edge modes (CMEMs) in a quantum anomalous hall/superconductor hybrid system. CMEM is predicted to induce a unique half quantized plateau as its transport signature[1–3]. This was recently found in the experiments[4]. However, is was argued that without superconductivity, disorder could also induce such signature[5, 6]. Here we proposed to use local tunneling spectroscopy to directly probe the edge state of the hybrid system. We used Recursive Green’s Function to show that for topological phase with Chern number N = ±1/2 which hosts 1/2 CMEM would have a dip or plateau in differential conductance measurements, respectively. We also compared the feature between the model simulation with recent experimental findings.

In Chapter 3, we consider superconductivity in multifold fermion metals. Taking Li2Pd3B and Li2Pt3B as examples, we find a large number of unconventional degenerate points, such as double spin-1, spin-3/2, Weyl and double Weyl topological band crossing points near the Fermi energy, which result in finite Chern numbers on Fermi surfaces. Long Fermi arc states in Li2Pd3B, originating from the nontrivial band topology are found. Importantly, it has been shown experimentally that Li2Pd3B and Li2Pt3B are fully gapped and gapless superconductors, respectively. By analyzing the possible pairing symmetries, we suggest that Li2Pd3B is a conventional s-wave superconductor or DIII class topological superconductor with Majorana surface states. Li2Pt3B, being gapless, is likely to be a nodal topological superconductor with dispersionless surface Majorana modes. We further identify that several other noncentrosymmetric superconductors, which serve as platforms for investigating the interplay between superconductivity and topologically nontrivial Fermi surfaces.

In Chapter 4, we study fractal superconductivity in a 2D Ando model with BCS superconductivity. Multifractal metal/insulator regions in the normal state are first identified by studying the two-eigen correlation function. With added superconductivity, Ifound the fractality in normal state gives risen to fractal superconductivity between homogeneous and granular case. With a enhanced mean pairing amplitude and multifractal statistics, Ishow that fractal superconductivity can be recognized by a convolutional neural network.

To request for meeting link, please write to phjacma@ust.hk.